2017/01/25 by Jiehua Chen, Chen, Jiehua, Ugo Finnendahl +2
Economics, Econometrics and Finance · Mathematics · Social Sciences · #Combinatorics (math.CO) #Economic theories and models #FOS: Mathematics #Game Theory and Voting Systems #Local Government Finance and Decentralization #math.CO
paper · pdf · doi:10.48550/arxiv.1701.08652
To appear in Discrete Mathematics
openalex publication_date 2017/01/25 · openalex created_date 2017/02/10 · arxiv created 2018/01/08 · arxiv updated 2018/01/09 · openalex updated_date 2026/07/28
We investigate preference profiles for a set V of voters, where each voter i has a preference order \succi on a finite set A of alternatives (that is, a linear order on A) such that for each two alternatives a,b∈ A, voter i prefers a to b if a\succi b. Such a profile is narcissistic if each alternative a is preferred the most by at least one voter. It is single-peaked if there is a linear order \trianglerightsp on the alternatives such that each voter's preferences on the alternatives along the order \trianglerightsp are either strictly increasing, or strictly decreasing, or first strictly increasing and then strictly decreasing. It is single-crossing if there is a linear order \trianglerightsc on the voters such that each pair of alternatives divides the order \trianglerightsc into at most two suborders, where in each suborder, all voters have the same linear order on this pair. We show that for n voters and n alternatives,the number of single-peaked narcissistic profiles is ∏i=2n-1 \binomn-1i-1 while the number of single-crossing narcissistic profiles is 2^\binomn-12.